Is it allowable for a sniper to set themselves up well back from a window (from inside a building) for a shot, even though by doing so they are sacrificing the 45 degree shooting arc in order to become much less of a target themselves?

I would suggest that the existing rules for spotting snipers - i.e. they are hard to spot - imply that the sniper is already following reasonable fieldcraft and firing from a relatively concealed position (e.g. within a room rather than at the window through which he or she is firing).

Thus I would say that it is over-complicating things to somehow try to make it harder to spot snipers in exchange for a narrower field of regard. But it's your game, of course, and YMMV.

Is it allowable for a sniper to set themselves up well back from a window (from inside a building) for a shot, even though by doing so they are sacrificing the 45 degree shooting arc in order to become much less of a target themselves?

That sounds like a bit of a house rule, no such option in the rule book.
I can't see the point of such placement in my opinion.
KISS
Normally we place a trooper in a firing position at the window , which gives him 45 degree from the middle of the window to each side that is a 90 angle of fire and to be spotted within that angle by enemy units.
To start the procedure of spotting a sniper, he must first fire.

I agree with agentbalzac. Setting yourself up in the shadows at the back of the room is basic fieldcraft, and something a good sniper should be doing anyway. Details like that are already built into the dice roll.

'Sniper' is what is shouted when any fool with a gun takes a single potshot at you, whether it's the movie 'guys up in the trees', a lone Hitler Youth with a rifle, or whatever. He has a standard weapon, typically using the sights that came with it and at a typical range of 0-300 metres. Quality is hit and miss depending on the individual concerned.

A WW2 sniper (with exceptions) is someone who has been picked from the ranks of men who qualified as marksmen, been sent on an advanced shooting course and typically has also received advanced fieldcraft tuition; he is usually then equipped with a specialised weapon, or a 'picked' average weapon, equipped with a telescopic sight. This allows him to engage accurately between 400 and 600 metres, with high hit probability and hardly any risk of being spotted, unless it's by another sniper.

Which do you suppose our guy with 50% hit probability and 16% chance of being spotted when he fires, represents? Snipers are abstracted for a reason and player control on their movement limited by the use of a CoC dice; it's so there's no shenanigans in play.